人字齿行星传动精度半解析建模与分析研究  

Modeling and Analysis of Transmission Accuracy of Semi-Analytical HerringboneGear Planetary Gear Train Considering Errors

作　　者：王腾达 董惠敏[1] 张楚 WANG Tengda;DONG Huimin;ZHANG Chu(School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学机械工程学院,大连116024

出　　处：《组合机床与自动化加工技术》2023年第9期21-25,共5页Modular Machine Tool & Automatic Manufacturing Technique

摘　　要：针对考虑误差的人字齿行星轮系传动精度求解的准确性与效率问题,提出一种人字齿行星轮系传动精度建模与分析的半解析方法,以便准确高效地分析制造误差对人字齿行星轮系传动精度的影响规律。基于切片法建立考虑齿距误差和双螺旋线对中误差的人字齿行星轮系准静态解析模型,人字齿轮内外齿轮副的柔度矩阵采用有限元子结构方法获得;通过迭代求解模型的非线性微分方程组分析行星传动在误差和负载作用下运动(位移/转角),形成半解析的人字齿行星轮系的传动精度分析方法;以3个行星轮的人字齿行星轮系为例,分析在负载工况下齿距偏差和双螺旋线对中误差对传动精度的影响,并在同等精度条件下与有限元对比提高计算效率300倍以上,说明本模型的有效性与准确性。Aiming at the accuracy and efficiency of solving the transmission accuracy of the herringbone planetary gear train considering the error,a semi-analytical method for modeling and analyzing the transmission accuracy of the herringbone planetary gear train is proposed to accurately and efficiently analyze the influence of manufacturing errors on the transmission accuracy of herringbone planetary gear train.Based on the slicing method,a quasi-static analytical model of the herringbone gear planetary gear train considering the pitch error and double helix alignment error is established,in which the compliance matrix of the inner and outer gear pairs of the herringbone gear is obtained by the finite element substructure method;The nonlinear differential equation system of the model analyzes the motion(displacement/rotation angle)of the planetary transmission under the action of error and load,and forms a semi-analytical method for analyzing the transmission accuracy of the herringbone planetary gear train;Taking the herringbone planetary gear train of three planetary gears as an example,the influence of pitch deviation and centering error of double helix on transmission accuracy under load condition is analyzed,and the calculation efficiency is more than 300 times higher than that of finite element under the same precision condition,which illustrates the validity and accuracy of this model.

关 键 词：人字齿行星轮系 分片法 半解析法 对中误差 传动精度 

分 类 号：TG122[金属学及工艺—金属学] TH165[机械工程—机械制造及自动化]